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P10.3 Forces and Braking

GCSE Combined Science · AQA · Chapter P10: Force and Motion

A free GCSE Combined Science: Trilogy lesson for AQA (8464) from OBA School: driving and resistive forces, stopping distance, reaction time, braking distance and braking force. Watch the video, read the explanation and worked examples, then try the revision questions. You can work through the full lesson, with every video, practice quizzes and printable worksheets with mark schemes, in our free online course.

What you will learn

  • Explain why the resultant force on a vehicle moving at a steady velocity is zero
  • Use stopping distance = thinking distance + braking distance, and calculate thinking distance from speed and reaction time
  • Describe the factors that affect reaction time and braking distance, and how reaction time can be measured
  • Explain how the brakes reduce the kinetic energy of a vehicle and why large decelerations are dangerous
  • (Higher tier) estimate the deceleration and braking force of a vehicle using v² − u² = 2 a s and F = m a

Key words

  • Driving force: The forward force on a vehicle produced by its engine or motor.
  • Resistive forces: Forces that oppose motion, mainly air resistance and friction.
  • Reaction time: The time between a driver seeing a hazard and starting to act, for example pressing the brake.
  • Thinking distance: The distance travelled during the driver’s reaction time.
  • Braking distance: The distance travelled while the braking force acts, until the vehicle stops.
  • Stopping distance: Thinking distance + braking distance.
  • Deceleration: Negative acceleration: the rate at which velocity decreases, in m/s².

Forces on a moving vehicle

A vehicle’s engine provides a driving force (friction of the road on the tyres). Resistive forces – mostly air resistance at high speeds, plus friction in moving parts – act against the motion.

  • Driving force = resistive forces: resultant force zero, constant velocity.
  • Driving force > resistive forces: the car accelerates.
  • Driving force < resistive forces (or brakes applied): the car decelerates.

Worked example: pulling away

A car of mass 1250 kg has a driving force of 3600 N and resistive forces of 850 N. Calculate its acceleration.
resultant force = 3600 − 850 = 2750 N; a = F ÷ m = 2750 ÷ 1250

Answer: a = 2.2 m/s²

Stopping distance

stopping distance = thinking distance + braking distance

During the reaction time the vehicle has not started to slow down, so:

thinking distance = speed × reaction time (thinking distance is directly proportional to speed)

Worked example: stopping from 22 m/s

A driver with a reaction time of 0.7 s is travelling at 22 m/s. The braking distance is 48.4 m.
thinking distance = 22 m/s × 0.7 s = 15.4 m
stopping distance = 15.4 m + 48.4 m

Answer: about 64 m

Key fact: Compare 10 m/s and 20 m/s in the chart: doubling the speed doubles the thinking distance (7 m → 14 m) but makes the braking distance four times bigger (10 m → 40 m).

Reaction time

Typical reaction times are between about 0.2 s and 0.9 s. Reaction time, and so thinking distance, is increased by:

  • tiredness
  • alcohol and some drugs (including some medicines – check the label)
  • distractions, such as using a mobile phone, listening to loud music or talking to passengers

Measuring reaction time with a ruler. A partner holds a ruler vertically with the zero mark between your open finger and thumb, then lets go without warning. You catch it as fast as you can. The further it falls, the longer your reaction time. Repeat several times and take a mean. The fall time can be found from the distance using t = √(2s ÷ g), which you will be given.

Worked example: ruler-drop result

A student catches the ruler after it has fallen 15 cm. Calculate her reaction time.
s = 0.15 m; t = √(2 × 0.15 ÷ 9.8) = √0.0306

Answer: t = 0.17 s

To test whether a distraction matters, repeat the test while the catcher talks or listens to music, keeping everything else (the same person, hand, ruler and drop height) the same.

Braking distance and braking energy

Braking distance is increased by:

  • higher speed (the biggest effect)
  • wet or icy roads: less friction between tyres and road, so the brakes must be applied more gently to avoid skidding
  • worn tyres (less grip) or worn brakes (less braking force); a smooth road surface also gives less grip
  • greater mass, for example a fully loaded van or a trailer

When the brakes are applied, friction between the brake pads and the discs does work on the wheels. This reduces the kinetic energy of the vehicle and transfers energy to the thermal store of the brakes, so their temperature rises.

work done by brakes = loss of kinetic energy: F × s = ½ m v²

Worked example: braking distance from energy

A 1400 kg car moving at 18 m/s brakes with a constant force of 7000 N. Calculate its braking distance.
Ek = ½ × 1400 × 18² = 226 800 J; s = Ek ÷ F = 226 800 ÷ 7000

Answer: s = 32.4 m

Very large decelerations are dangerous: the brakes can overheat, the wheels can lock and skid, the driver can lose control, and people inside are thrown forward with large forces.

Estimating deceleration and braking force (Higher tier)

For a vehicle that stops (v = 0) from initial speed u in braking distance s, the equation v² − u² = 2 a s gives a = −u² ÷ 2s (the minus sign shows a deceleration). Then the braking force is F = m a.

Worked example: braking force on a car

A car of mass 1300 kg travelling at 24 m/s stops in a braking distance of 40 m.
a = −24² ÷ (2 × 40) = −576 ÷ 80 = −7.2 m/s²; F = m a = 1300 × 7.2 = 9360 N

Answer: deceleration 7.2 m/s²; braking force about 9.4 kN

Useful estimates: a car has a mass of roughly 1000–1500 kg; a fully loaded lorry about 40 000 kg. On a dry road a car can decelerate at about 6–8 m/s² without skidding, so braking forces range from several kilonewtons for a car to hundreds of kilonewtons for a heavy lorry.

Common mistakes

  • Saying tiredness or alcohol increases the braking distance. They increase reaction time, so they increase the thinking distance.
  • Saying wet roads or worn tyres increase the thinking distance. They increase the braking distance.
  • Assuming that doubling the speed doubles the braking distance. It makes it about four times longer.
  • Forgetting to convert a reaction time in milliseconds to seconds (700 ms = 0.7 s).

Revision questions

Try these, then check your answers below each one.

Question 1. A driver travelling at 25 m/s has a reaction time of 0.60 s. Calculate her thinking distance.

Answer: 15 m

Working: Thinking distance = speed × reaction time = 25 × 0.60 = 15 m.

Question 2. Which of these increases the thinking distance of a driver? (Choose from: Being tired, An icy road, Worn tyres, Worn brakes.)

Answer: Being tired

Working: Tiredness increases reaction time, so it increases thinking distance. The other three increase braking distance.

Question 3. True or false? If a car’s speed doubles, its braking distance doubles.

Answer: False

Working: False. With the same braking force, doubling the speed makes the kinetic energy four times bigger, so the braking distance is about four times longer.

Related lessons

Continue in the full course

This lesson is section P10.3 (AGCSC3903) of our free GCSE Combined Science course for AQA. In the full course you get every video for this section, a self-marking practice quiz, a printable worksheet with a mark scheme, chapter tests, and your progress saved. Go to the full GCSE Combined Science course.

 

 

 

 

 

 

 

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